What is the Archbishop of Canterbury for? That is the question Rowan Williams leaves behind as he heads off to Cambridge. When he took office, he was widely thought to be a good thing, and a good man, and the question didn’t at first present itself.

Generally agreed to be a liberal intellectual, an independent thinker and a man of great moral integrity, he seemed quite likely to do a reasonable job as archbishop, whatever that means. In the event he has proved to be a great disappointment to all kinds of people inside and outside the Anglican tribe. He leaves behind more anger and division in the church than he found. Worse than that, he has managed to bring into sharp relief one of the few things it is certainly the job of an archbishop to obscure — the awkward question of the disestablishment of the Church of England.

Admittedly Williams became archbishop at an exceptionally difficult time. Whatever he did or failed to do, the bitter division in the church about homosexual bishops was certain to split it, sooner or later. There is no compromise possible between those who will not accept gay priests, or indeed those African Anglicans who despise homosexuals, and those who share Williams’s acceptance of them as equals. There are too many other views and feelings within the church that are wholly at odds with each other, such as the ordination of women. Leading the Church of England must be like herding ferrets: the job is impossible, as things stand.

Williams might have been the man for the hour, full of radical integrity as he was supposed to be. However, the first signs were not good. For instance, he had made it clear he believed that invading Iraq would be immoral and illegal. Whether or not one agreed, that was and is a reasonable moral view. However, no sooner had he been appointed archbishop than he said that he would in fact support military action in Iraq but only if it were cleared by the United Nations.

This defies belief. Here was a spiritual leader from a free and open society, known for his holiness, saying that something is morally wrong unless the United Nations says it’s okay. Williams had described himself as given to asking awkward questions, but clearly he had not asked many about the UN — that collection of kleptocrats, autocrats, mass murderers and horse-traders. Besides, it is the duty of a spiritual leader to lead, not to vacillate. For, as the Bible says, “if the trumpet give an uncertain sound, who shall prepare himself to the battle” — the battle here being for the integrity of the Anglican church.

Williams’s disastrous comments about sharia were a revelation of his unfitness for office There has been something consistently uncertain about the sounds Williams makes. He will sometimes denounce something only weeks after having supported it: his very public attack on Cameron’s big society policy came only a few months after openly praising it.

Even his admirers accuse him of drawing out long negotiations with verbiage. Sometimes his pronouncements are mind-bendingly opaque. What he writes can be so badly put and difficult to understand that it makes one question his supposed cleverness: surely clarity is the sign of a good mind. Yet one of his clerical friends coyly praises his “carefully judged opacity” — not the mark of a man of integrity, surely.

At other times Williams has simply compromised his own beliefs. Long before he came to office he made this promise to gay Christians at the Lambeth conference of 1998: “We pledge we will continue to reflect, pray and work for your full inclusion in the life of the church.” He may well have done a lot of praying and reflecting, but today this looks like a promise he did not keep. Politically that’s understandable for an archbishop determined to keep the church united, impossible though that must be.

What is not understandable morally is his treatment of Jeffrey John, a gay canon whose appointment as suffragan bishop of Reading Williams had approved in 2003. Soon afterwards, under pressure from aggressive anti-gay Anglicans and their allies among the bishops, Williams, together with John Sentamu, Archbishop of York, forced Jeffrey John to stand down, to give up his bishopric. That was bad enough but — according to the late Colin Slee, the former dean of Southwark — it was done with shocking unkindness and bullying over two miserable days. This was not just pusillanimous; it was cruel of both men.

So here we had a woolly-faced, woolly-minded, wordy man of inconsistent and incoherent views presiding over a miserably divided church. However, that didn’t seem to matter, broadly speaking. The usual English muddle might continue for years.

However, all that changed with Williams’s disastrous comments about sharia in 2008. It was a truly astonishing revelation of his unfitness for his office. He actually said that we must “face up to the fact” that some British citizens do not relate to the British legal system and that Muslims should not have to choose between “the stark alternatives of cultural loyalty or state loyalty”. Worse was to come. He went on to say that, although the ideal situation is one in which there is one and only one law for everybody, a pillar of Western democracy, nonetheless at the same time this very pillar — well, “I think that’s a bit of a danger”.

The danger is Williams himself. If the Archbishop of Canterbury will not uphold the principle of equality under the law, and actually questions it ex officio, he has become a social menace. Through this and his other woolly-minded meddling in politics, lacking any mandate but using his privileged religious position within the establishment to do so, he has encouraged other religious leaders to feel they have the right to do the same. That is very dangerous.

If members of a small, dwindling minority faith such as the C of E can have seats in the Lords and ritual authority, why not all other faiths? Some of those other faiths are growing fast — perhaps, in the name of equal representation, they should have more seats than the fading Anglican bishops. The antics of the Archbishop of Canterbury have made that question unavoidable. And the best answer to the question is the disestablishment of the Church of England.

Perhaps that is what the opaque, faintly comic archbishop really achieved — inadvertently to create an awareness that the Church of England must be disestablished. Williams has turned out to be the Mr Pooter of the Anglican Götterdämmerung.